It is known that any Lévy process \(L_t, t \ge 0,\)  can be represented in the form \(L_t=\mu t + \sigma W_t +J_t\) , where \(J_t\)  is a pure-jump process, see [1]}. As it is shown in many papers (see the references in the introduction), the statistical inference for this general case is rather complicated, provided that the Lévy measure of \(J_t\)  may be infinite and only the low-frequency data are available. Indeed, in this case it is difficult to distinguish the small jumps of \(J_t\)  from the continuous part \(\mu t +\sigma W_t\) , since the changes over time interval of the fixed length \(\Delta \)  can be caused both by a jump or by the continuous part. Taking into account this fact, we concentrate on the Lévy processes with finite Lévy measure, that is, on the processes in the form (REF ).
